A novel differential kinematics model to compare the kinematic performances of 5-axis CNC machines

A 5-axis CNC machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool. The 5-axis CNC machines are designed in a large variety of kinematic configurations and structures. Comparing different 5-axis kinematic configurations plays an important role in machine selection and optimal machine design. In this sense, the present study proposes a new mathematical model to analyze and compare the kinematic performances of the 5-axis machines. First, a generalized kinematic chain of 5-axis machine is treated as a unified kinematic chain of two collaborative robots in order to formulate a generalized differential kinematics model of the machines. Second, four important properties of the kinematics model are proved in a generalized case so that quantitative parameters characterizing the kinematic performances of the machines can be evaluated effectively. Last, six typical groups of 5-axis CNC configurations are compared through the evaluated parameters. In addition, it has been shown that, by using the properties of the kinematics model, the forward and inverse kinematic equations for the rotary axes of any 5-axis machine can be formulated in an effective and simplified manner that could be useful for developing the postprocessors for any 5-axis machine.